Result: An improvement on perturbation bounds for the Drazin inverse: An improvement on perturbation bounds for the Drazin inverse.

Title:
An improvement on perturbation bounds for the Drazin inverse: An improvement on perturbation bounds for the Drazin inverse.
Authors:
Wei, Yimin, Li, Xiezhang
Source:
Numerical Linear Algebra with Applications. 10:563-575
Publisher Information:
Wiley, 2003.
Publication Year:
2003
Subject Terms:
oblique projection, 4. Education, Other matrix algorithms, perturbation bounds, Theory of matrix inversion and generalized inverses, Drazin inverse, 0101 mathematics, Square Matrix, Drazin Inverse, 01 natural sciences, Mathematics, Perturbation, Education
Document Type:
Academic journal Article
File Description:
application/xml
Language:
English
ISSN:
1099-1506
1070-5325
DOI:
10.1002/nla.336
Access URL:
https://zbmath.org/2206750
https://doi.org/10.1002/nla.336
Rights:
Wiley Online Library User Agreement
Accession Number:
edsair.doi.dedup.....b6fceb45abaf3266c30ebe1ae78bb577
Database:
OpenAIRE

Further Information

The Drazin inverse of a square matrix occurs in a number of applications. It is of importance to analyse the perturbation bounds for the Drazin inverse of a matrix. Let B=A+E. Under the assumption of rank(Bj) =rank(Ak), where j and k are the indices of B and A, respectively, upper bounds of ∥BD‐AD∥/∥AD∥ and ∥BBD‐AAD∥/∥AAD∥ have been recently studied. However, these upper bounds do not cover the perturbation bounds of the group inverse recently given by the authors as a special case.Moreover, these perturbation bounds for the Drazin inverse are too large to be practical. In this paper, we present sharper unified perturbation bounds for the Drazin inverse, which are the extensions of the recent result in the case of group inverse. It solves the problem posed by Campbell and Meyer in 1975. A numerical example is given to illustrate the sharpness of the new general bounds. Copyright © 2003 John Wiley & Sons, Ltd.